12n
0755
(K12n
0755
)
A knot diagram
1
Linearized knot diagam
4 6 8 9 3 10 2 12 7 5 8 9
Solving Sequence
9,12 1,5
4 2 8 3 7 11 10 6
c
12
c
4
c
1
c
8
c
3
c
7
c
11
c
10
c
6
c
2
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h1.18568 × 10
223
u
81
+ 7.43164 × 10
223
u
80
+ ··· + 3.23988 × 10
222
b + 4.31116 × 10
223
,
− 1.92883 × 10
223
u
81
− 1.27832 × 10
224
u
80
+ ··· + 3.23988 × 10
222
a − 1.11257 × 10
224
,
u
82
+ 6u
81
+ ··· − 11u − 3i
I
u
2
= h−1890866592561u
22
+ 2410031480209u
21
+ ··· + 3200805062239b + 12377780689946,
− 7028112561663u
22
+ 3451841046935u
21
+ ··· + 3200805062239a + 16799928060287,
u
23
− u
22
+ ··· − 3u + 1i
* 2 irreducible components of dim
C
= 0, with total 105 representations.
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I. I
u
1
= h1.19 × 10
223
u
81
+ 7.43 × 10
223
u
80
+ · · · + 3.24 × 10
222
b + 4.31 ×
10
223
, −1.93 × 10
223
u
81
− 1.28 × 10
224
u
80
+ · · · + 3.24 × 10
222
a − 1.11 ×
10
224
, u
82
+ 6u
81
+ · · · − 11u − 3i
(i) Arc colorings
a
9
=
0
u
a
12
=
1
0
a
1
=
1
u
2
a
5
=
5.95340u
81
+ 39.4558u
80
+ ··· + 211.539u + 34.3399
−3.65962u
81
− 22.9380u
80
+ ··· − 108.880u − 13.3065
a
4
=
5.95340u
81
+ 39.4558u
80
+ ··· + 211.539u + 34.3399
−2.25036u
81
− 13.4360u
80
+ ··· − 49.9298u − 2.10025
a
2
=
2.45651u
81
+ 13.4972u
80
+ ··· + 8.18878u − 15.0013
3.58310u
81
+ 22.9490u
80
+ ··· + 93.7957u + 10.9838
a
8
=
u
u
a
3
=
4.36051u
81
+ 28.9039u
80
+ ··· + 146.566u + 23.3322
−3.84325u
81
− 23.9879u
80
+ ··· − 114.903u − 13.1080
a
7
=
0.731709u
81
+ 7.25277u
80
+ ··· + 134.322u + 45.5660
−3.38808u
81
− 21.7865u
80
+ ··· − 116.411u − 20.2879
a
11
=
−u
2
+ 1
−u
2
a
10
=
1.23820u
81
+ 5.64993u
80
+ ··· − 58.9501u − 27.1169
2.72175u
81
+ 17.1903u
80
+ ··· + 62.3171u + 5.29688
a
6
=
1.96680u
81
+ 15.0496u
80
+ ··· + 138.404u + 35.1527
−4.97606u
81
− 31.6255u
80
+ ··· − 132.203u − 16.3332
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4.04743u
81
− 27.0123u
80
+ ··· − 215.823u − 51.0412
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
82
− 4u
81
+ ··· − 14492u + 15032
c
2
, c
5
u
82
− 2u
81
+ ··· + 386u − 21
c
3
u
82
− 2u
81
+ ··· − 9468926u − 944291
c
4
u
82
+ u
81
+ ··· + 12069u + 3617
c
6
, c
9
u
82
+ u
81
+ ··· + 403u + 61
c
7
u
82
+ 2u
81
+ ··· + 28u − 151
c
8
, c
11
, c
12
u
82
+ 6u
81
+ ··· − 11u − 3
c
10
u
82
− u
81
+ ··· − 2699225u + 632501
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
82
+ 70y
81
+ ··· + 3143561008y + 225961024
c
2
, c
5
y
82
+ 52y
81
+ ··· − 12412y + 441
c
3
y
82
+ 48y
81
+ ··· − 10989606497604y + 891685492681
c
4
y
82
− 71y
81
+ ··· − 240578075y + 13082689
c
6
, c
9
y
82
+ 47y
81
+ ··· + 37305y + 3721
c
7
y
82
+ 4y
81
+ ··· − 246310y + 22801
c
8
, c
11
, c
12
y
82
− 18y
81
+ ··· − 397y + 9
c
10
y
82
− 45y
81
+ ··· − 21983555058121y + 400057515001
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.806236 + 0.447979I
a = 0.116844 + 0.907734I
b = 0.313050 + 0.872682I
−0.042747 + 1.373590I 0
u = −0.806236 − 0.447979I
a = 0.116844 − 0.907734I
b = 0.313050 − 0.872682I
−0.042747 − 1.373590I 0
u = 0.835911 + 0.366396I
a = −0.895782 − 0.543357I
b = 0.686491 + 0.523534I
1.47647 − 3.78347I 0
u = 0.835911 − 0.366396I
a = −0.895782 + 0.543357I
b = 0.686491 − 0.523534I
1.47647 + 3.78347I 0
u = −0.701050 + 0.577627I
a = −0.094098 + 0.689287I
b = 0.443176 + 0.530379I
−0.048198 + 1.306660I 0
u = −0.701050 − 0.577627I
a = −0.094098 − 0.689287I
b = 0.443176 − 0.530379I
−0.048198 − 1.306660I 0
u = −0.874548 + 0.018157I
a = −1.53808 + 0.49342I
b = 1.016920 − 0.505156I
−1.58786 + 5.67587I −9.37818 − 5.48357I
u = −0.874548 − 0.018157I
a = −1.53808 − 0.49342I
b = 1.016920 + 0.505156I
−1.58786 − 5.67587I −9.37818 + 5.48357I
u = −1.15383
a = −0.365134
b = −0.413477
−2.52087 0
u = −0.750355 + 0.898180I
a = −0.25763 − 1.49046I
b = 0.73558 − 1.48679I
7.24531 + 4.47737I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.750355 − 0.898180I
a = −0.25763 + 1.49046I
b = 0.73558 + 1.48679I
7.24531 − 4.47737I 0
u = −0.425248 + 1.099560I
a = 0.45745 + 1.56142I
b = −0.381257 + 0.936714I
3.38750 + 5.56328I 0
u = −0.425248 − 1.099560I
a = 0.45745 − 1.56142I
b = −0.381257 − 0.936714I
3.38750 − 5.56328I 0
u = −0.821348 + 0.914226I
a = −0.931141 − 0.836821I
b = −0.24212 − 1.51037I
2.05800 − 4.23861I 0
u = −0.821348 − 0.914226I
a = −0.931141 + 0.836821I
b = −0.24212 + 1.51037I
2.05800 + 4.23861I 0
u = 0.822864 + 0.959472I
a = −0.58005 + 1.29619I
b = 0.60803 + 1.79418I
7.49350 − 0.72833I 0
u = 0.822864 − 0.959472I
a = −0.58005 − 1.29619I
b = 0.60803 − 1.79418I
7.49350 + 0.72833I 0
u = −0.673993 + 0.279521I
a = −0.540764 + 0.727882I
b = −1.64438 + 0.06585I
−3.58880 + 2.02013I −13.3165 − 8.2924I
u = −0.673993 − 0.279521I
a = −0.540764 − 0.727882I
b = −1.64438 − 0.06585I
−3.58880 − 2.02013I −13.3165 + 8.2924I
u = 0.883514 + 0.916466I
a = −0.822379 + 0.907210I
b = 0.16986 + 1.49068I
4.92220 − 0.58301I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.883514 − 0.916466I
a = −0.822379 − 0.907210I
b = 0.16986 − 1.49068I
4.92220 + 0.58301I 0
u = −0.631826 + 0.348866I
a = 0.61391 + 2.12275I
b = −1.108410 + 0.201294I
−3.40457 + 0.57973I −9.43437 − 4.19864I
u = −0.631826 − 0.348866I
a = 0.61391 − 2.12275I
b = −1.108410 − 0.201294I
−3.40457 − 0.57973I −9.43437 + 4.19864I
u = 0.712432 + 0.084214I
a = 0.58489 − 1.49460I
b = 0.40860 − 1.43638I
−1.50757 − 6.70450I −11.21324 + 6.26401I
u = 0.712432 − 0.084214I
a = 0.58489 + 1.49460I
b = 0.40860 + 1.43638I
−1.50757 + 6.70450I −11.21324 − 6.26401I
u = −0.450661 + 0.549059I
a = 0.283735 − 0.371733I
b = 1.99582 + 0.12483I
0.42096 + 8.02120I −2.11051 − 11.91858I
u = −0.450661 − 0.549059I
a = 0.283735 + 0.371733I
b = 1.99582 − 0.12483I
0.42096 − 8.02120I −2.11051 + 11.91858I
u = −0.974900 + 0.848966I
a = −0.773538 − 0.899541I
b = 0.564453 − 1.073860I
0.47523 + 4.56353I 0
u = −0.974900 − 0.848966I
a = −0.773538 + 0.899541I
b = 0.564453 + 1.073860I
0.47523 − 4.56353I 0
u = −0.950851 + 0.883034I
a = 0.330778 + 0.966106I
b = −0.132030 + 1.199490I
0.53361 + 1.91658I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.950851 − 0.883034I
a = 0.330778 − 0.966106I
b = −0.132030 − 1.199490I
0.53361 − 1.91658I 0
u = −0.065661 + 0.689575I
a = 0.188975 − 0.904470I
b = −0.618127 + 0.219610I
0.90992 + 2.47162I −2.89492 − 3.06151I
u = −0.065661 − 0.689575I
a = 0.188975 + 0.904470I
b = −0.618127 − 0.219610I
0.90992 − 2.47162I −2.89492 + 3.06151I
u = −0.582300 + 1.190720I
a = −0.159473 − 0.797913I
b = 0.03486 − 1.72869I
6.45996 + 1.18643I 0
u = −0.582300 − 1.190720I
a = −0.159473 + 0.797913I
b = 0.03486 + 1.72869I
6.45996 − 1.18643I 0
u = −1.098680 + 0.754147I
a = 1.002280 + 0.473388I
b = 0.219617 + 1.329070I
6.12437 + 1.73968I 0
u = −1.098680 − 0.754147I
a = 1.002280 − 0.473388I
b = 0.219617 − 1.329070I
6.12437 − 1.73968I 0
u = −0.260067 + 0.609056I
a = 1.90359 − 0.34249I
b = −0.049741 − 0.351548I
3.81108 + 2.73141I 4.36589 − 2.14562I
u = −0.260067 − 0.609056I
a = 1.90359 + 0.34249I
b = −0.049741 + 0.351548I
3.81108 − 2.73141I 4.36589 + 2.14562I
u = −1.018490 + 0.869250I
a = 0.60257 + 1.28317I
b = −0.78229 + 1.66142I
1.48594 + 10.83750I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.018490 − 0.869250I
a = 0.60257 − 1.28317I
b = −0.78229 − 1.66142I
1.48594 − 10.83750I 0
u = 1.005000 + 0.889070I
a = 0.603105 − 1.085290I
b = −0.46354 − 1.66659I
4.55738 − 6.10859I 0
u = 1.005000 − 0.889070I
a = 0.603105 + 1.085290I
b = −0.46354 + 1.66659I
4.55738 + 6.10859I 0
u = 0.520783 + 0.400279I
a = −0.419662 + 0.443731I
b = 1.48234 + 0.41015I
2.58165 − 3.80058I 2.24184 + 7.84876I
u = 0.520783 − 0.400279I
a = −0.419662 − 0.443731I
b = 1.48234 − 0.41015I
2.58165 + 3.80058I 2.24184 − 7.84876I
u = 0.626125 + 0.145468I
a = −0.18087 − 2.79944I
b = −0.587182 + 0.101724I
−4.14051 − 1.50707I −13.3689 + 5.4539I
u = 0.626125 − 0.145468I
a = −0.18087 + 2.79944I
b = −0.587182 − 0.101724I
−4.14051 + 1.50707I −13.3689 − 5.4539I
u = 1.063340 + 0.849536I
a = 0.956780 − 0.757979I
b = −0.03841 − 1.76406I
6.72056 − 5.96162I 0
u = 1.063340 − 0.849536I
a = 0.956780 + 0.757979I
b = −0.03841 + 1.76406I
6.72056 + 5.96162I 0
u = 0.476810 + 0.402159I
a = 2.10026 + 2.83473I
b = 0.284676 + 0.060377I
−0.29800 − 7.98807I −3.3717 + 15.3963I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.476810 − 0.402159I
a = 2.10026 − 2.83473I
b = 0.284676 − 0.060377I
−0.29800 + 7.98807I −3.3717 − 15.3963I
u = −0.387572 + 0.483892I
a = −0.506786 + 0.595374I
b = 0.161400 + 0.343252I
−0.209152 + 1.137760I −2.77451 − 5.70461I
u = −0.387572 − 0.483892I
a = −0.506786 − 0.595374I
b = 0.161400 − 0.343252I
−0.209152 − 1.137760I −2.77451 + 5.70461I
u = 0.557426 + 0.231728I
a = −0.33867 − 1.76399I
b = −1.10016 − 1.23923I
−3.82873 − 0.00668I −16.1459 + 7.0292I
u = 0.557426 − 0.231728I
a = −0.33867 + 1.76399I
b = −1.10016 + 1.23923I
−3.82873 + 0.00668I −16.1459 − 7.0292I
u = 1.409430 + 0.115816I
a = −0.164334 + 0.187390I
b = −0.135012 − 0.469782I
−6.54986 − 3.23861I 0
u = 1.409430 − 0.115816I
a = −0.164334 − 0.187390I
b = −0.135012 + 0.469782I
−6.54986 + 3.23861I 0
u = 0.84939 + 1.16040I
a = 0.631650 − 0.921823I
b = 0.03685 − 1.45118I
9.67520 + 3.07500I 0
u = 0.84939 − 1.16040I
a = 0.631650 + 0.921823I
b = 0.03685 + 1.45118I
9.67520 − 3.07500I 0
u = −0.98461 + 1.06132I
a = −0.518913 − 1.125470I
b = 0.359482 − 1.003890I
0.93021 + 4.88868I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.98461 − 1.06132I
a = −0.518913 + 1.125470I
b = 0.359482 + 1.003890I
0.93021 − 4.88868I 0
u = −0.86125 + 1.16514I
a = 0.705142 + 0.791235I
b = 0.19060 + 1.59932I
6.48875 − 9.64645I 0
u = −0.86125 − 1.16514I
a = 0.705142 − 0.791235I
b = 0.19060 − 1.59932I
6.48875 + 9.64645I 0
u = 0.82211 + 1.22177I
a = −0.397179 + 0.816867I
b = 0.40067 + 1.95196I
6.25873 − 3.82475I 0
u = 0.82211 − 1.22177I
a = −0.397179 − 0.816867I
b = 0.40067 − 1.95196I
6.25873 + 3.82475I 0
u = 0.510704 + 0.080688I
a = −1.91916 + 0.40206I
b = 0.714917 + 0.882843I
2.50196 − 2.66858I −1.26207 + 3.93369I
u = 0.510704 − 0.080688I
a = −1.91916 − 0.40206I
b = 0.714917 − 0.882843I
2.50196 + 2.66858I −1.26207 − 3.93369I
u = −1.13264 + 0.96131I
a = −0.573896 − 1.114140I
b = 0.77313 − 1.68807I
5.5638 + 17.2835I 0
u = −1.13264 − 0.96131I
a = −0.573896 + 1.114140I
b = 0.77313 + 1.68807I
5.5638 − 17.2835I 0
u = 1.13751 + 0.96101I
a = −0.573662 + 1.059270I
b = 0.54430 + 1.58374I
8.71424 − 10.69960I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.13751 − 0.96101I
a = −0.573662 − 1.059270I
b = 0.54430 − 1.58374I
8.71424 + 10.69960I 0
u = −1.48390 + 0.24377I
a = −0.031323 − 0.358276I
b = −0.235266 − 0.710195I
−1.098920 + 0.366529I 0
u = −1.48390 − 0.24377I
a = −0.031323 + 0.358276I
b = −0.235266 + 0.710195I
−1.098920 − 0.366529I 0
u = 0.492926
a = 1.00800
b = −1.10716
−1.69272 −3.43940
u = 1.11375 + 1.03431I
a = 0.577088 − 0.734092I
b = −0.56145 − 1.82423I
5.35450 − 4.18150I 0
u = 1.11375 − 1.03431I
a = 0.577088 + 0.734092I
b = −0.56145 + 1.82423I
5.35450 + 4.18150I 0
u = 1.54442 + 0.24643I
a = 0.217680 + 0.007983I
b = −0.345847 + 0.430990I
−4.74804 − 6.73053I 0
u = 1.54442 − 0.24643I
a = 0.217680 − 0.007983I
b = −0.345847 − 0.430990I
−4.74804 + 6.73053I 0
u = −1.28649 + 0.97876I
a = 0.566181 + 0.565715I
b = −0.75720 + 1.37954I
4.36428 + 6.64097I 0
u = −1.28649 − 0.97876I
a = 0.566181 − 0.565715I
b = −0.75720 − 1.37954I
4.36428 − 6.64097I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.338398 + 0.065785I
a = −3.21361 + 0.05803I
b = −0.202094 + 0.875685I
0.77876 + 2.17059I −3.05306 − 2.50525I
u = −0.338398 − 0.065785I
a = −3.21361 − 0.05803I
b = −0.202094 − 0.875685I
0.77876 − 2.17059I −3.05306 + 2.50525I
13
II.
I
u
2
= h−1.89×10
12
u
22
+2.41×10
12
u
21
+· · ·+3.20×10
12
b+1.24×10
13
, −7.03×
10
12
u
22
+3.45×10
12
u
21
+· · ·+3.20×10
12
a+1.68×10
13
, u
23
−u
22
+· · ·−3u+1i
(i) Arc colorings
a
9
=
0
u
a
12
=
1
0
a
1
=
1
u
2
a
5
=
2.19573u
22
− 1.07843u
21
+ ··· + 7.61282u − 5.24866
0.590747u
22
− 0.752945u
21
+ ··· + 2.18120u − 3.86708
a
4
=
2.19573u
22
− 1.07843u
21
+ ··· + 7.61282u − 5.24866
0.977901u
22
− 0.852039u
21
+ ··· + 3.33738u − 4.98439
a
2
=
−4.02910u
22
+ 1.11016u
21
+ ··· − 18.5602u + 6.75980
−3.12743u
22
+ 1.87545u
21
+ ··· − 8.95195u + 6.59751
a
8
=
u
u
a
3
=
1.84688u
22
− 1.23642u
21
+ ··· + 5.85633u − 4.25721
0.629049u
22
− 1.01003u
21
+ ··· + 1.58088u − 3.99294
a
7
=
4.27517u
22
− 1.90167u
21
+ ··· + 10.9963u − 7.43747
0.325782u
22
+ 0.886134u
21
+ ··· + 7.99290u − 4.83426
a
11
=
−u
2
+ 1
−u
2
a
10
=
−2.56863u
22
+ 0.695455u
21
+ ··· − 13.1510u + 1.06396
−2.57971u
22
+ 1.28620u
21
+ ··· − 9.48726u + 5.94213
a
6
=
−0.598057u
22
+ 1.30233u
21
+ ··· + 4.71204u + 5.08438
1.69862u
22
+ 0.393112u
21
+ ··· + 15.8887u − 6.69634
(ii) Obstruction class = 1
(iii) Cusp Shapes
=
36632544074525
3200805062239
u
22
−
23085135423462
3200805062239
u
21
+ ··· +
89601441698510
3200805062239
u −
81515705395485
3200805062239
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
23
− u
22
+ ··· + 4u
2
− 1
c
2
u
23
− 9u
22
+ ··· + 88u − 11
c
3
u
23
− u
22
+ ··· − u
2
− 1
c
4
u
23
− 3u
21
+ ··· + 5u + 1
c
5
u
23
+ 9u
22
+ ··· + 88u + 11
c
6
u
23
+ 8u
21
+ ··· + u − 1
c
7
u
23
− u
22
+ ··· − 4u + 1
c
8
u
23
+ u
22
+ ··· − 3u − 1
c
9
u
23
+ 8u
21
+ ··· + u + 1
c
10
u
23
− 8u
21
+ ··· + 13u − 1
c
11
, c
12
u
23
− u
22
+ ··· − 3u + 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
23
+ 7y
22
+ ··· + 8y −1
c
2
, c
5
y
23
+ 13y
22
+ ··· − 418y −121
c
3
y
23
+ 9y
22
+ ··· − 2y −1
c
4
y
23
− 6y
22
+ ··· + 17y −1
c
6
, c
9
y
23
+ 16y
22
+ ··· + y −1
c
7
y
23
− 7y
22
+ ··· − 8y −1
c
8
, c
11
, c
12
y
23
− 13y
22
+ ··· + 19y −1
c
10
y
23
− 16y
22
+ ··· + 67y −1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.04348
a = 0.186091
b = 0.753788
−2.87298 −18.0690
u = −0.664063 + 0.943098I
a = 0.685970 + 0.966250I
b = −0.569285 + 0.905311I
3.29876 + 4.65028I −0.98001 − 3.86096I
u = −0.664063 − 0.943098I
a = 0.685970 − 0.966250I
b = −0.569285 − 0.905311I
3.29876 − 4.65028I −0.98001 + 3.86096I
u = −0.651688 + 0.414639I
a = 0.336676 − 1.276670I
b = 1.189520 − 0.108095I
−2.78319 + 1.65732I −2.40871 − 5.71074I
u = −0.651688 − 0.414639I
a = 0.336676 + 1.276670I
b = 1.189520 + 0.108095I
−2.78319 − 1.65732I −2.40871 + 5.71074I
u = −0.681262 + 0.184332I
a = 0.569301 − 0.688734I
b = −1.062700 + 0.406261I
2.16743 + 3.23271I −3.58442 + 1.29756I
u = −0.681262 − 0.184332I
a = 0.569301 + 0.688734I
b = −1.062700 − 0.406261I
2.16743 − 3.23271I −3.58442 − 1.29756I
u = 0.694058 + 1.101970I
a = 0.255791 − 1.003080I
b = −0.45605 − 1.81744I
6.42155 − 2.33889I −0.62038 + 2.50500I
u = 0.694058 − 1.101970I
a = 0.255791 + 1.003080I
b = −0.45605 + 1.81744I
6.42155 + 2.33889I −0.62038 − 2.50500I
u = −0.941533 + 0.914490I
a = −0.826024 − 1.090000I
b = 0.417785 − 0.988387I
1.36751 + 4.63600I 3.14920 − 3.22216I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.941533 − 0.914490I
a = −0.826024 + 1.090000I
b = 0.417785 + 0.988387I
1.36751 − 4.63600I 3.14920 + 3.22216I
u = 1.313860 + 0.211685I
a = 0.251038 + 0.443133I
b = 0.427917 − 0.312916I
−6.88091 − 2.68742I −11.27297 − 1.77001I
u = 1.313860 − 0.211685I
a = 0.251038 − 0.443133I
b = 0.427917 + 0.312916I
−6.88091 + 2.68742I −11.27297 + 1.77001I
u = −1.44708 + 0.16614I
a = 0.224237 + 0.573848I
b = 0.090985 + 0.602410I
−1.37900 + 0.85896I −12.3793 − 7.8029I
u = −1.44708 − 0.16614I
a = 0.224237 − 0.573848I
b = 0.090985 − 0.602410I
−1.37900 − 0.85896I −12.3793 + 7.8029I
u = 1.45654 + 0.11386I
a = 0.228446 − 0.393877I
b = −0.459533 − 0.102140I
−5.18757 − 7.22928I −10.56655 + 8.90804I
u = 1.45654 − 0.11386I
a = 0.228446 + 0.393877I
b = −0.459533 + 0.102140I
−5.18757 + 7.22928I −10.56655 − 8.90804I
u = 1.12449 + 0.97445I
a = −0.667965 + 0.669158I
b = 0.42725 + 1.78877I
5.14593 − 5.17174I −3.71472 + 6.91746I
u = 1.12449 − 0.97445I
a = −0.667965 − 0.669158I
b = 0.42725 − 1.78877I
5.14593 + 5.17174I −3.71472 − 6.91746I
u = 0.414919 + 0.284656I
a = 0.70756 + 2.63982I
b = 1.083190 + 0.759470I
−3.50970 + 0.39783I −5.42174 − 5.80351I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.414919 − 0.284656I
a = 0.70756 − 2.63982I
b = 1.083190 − 0.759470I
−3.50970 − 0.39783I −5.42174 + 5.80351I
u = 0.403492 + 0.147341I
a = 1.14193 + 2.95973I
b = −0.965980 + 0.449954I
−0.51419 − 7.27979I −6.66615 + 5.52222I
u = 0.403492 − 0.147341I
a = 1.14193 − 2.95973I
b = −0.965980 − 0.449954I
−0.51419 + 7.27979I −6.66615 − 5.52222I
19
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
23
− u
22
+ ··· + 4u
2
− 1)(u
82
− 4u
81
+ ··· − 14492u + 15032)
c
2
(u
23
− 9u
22
+ ··· + 88u − 11)(u
82
− 2u
81
+ ··· + 386u − 21)
c
3
(u
23
− u
22
+ ··· − u
2
− 1)(u
82
− 2u
81
+ ··· − 9468926u − 944291)
c
4
(u
23
− 3u
21
+ ··· + 5u + 1)(u
82
+ u
81
+ ··· + 12069u + 3617)
c
5
(u
23
+ 9u
22
+ ··· + 88u + 11)(u
82
− 2u
81
+ ··· + 386u − 21)
c
6
(u
23
+ 8u
21
+ ··· + u − 1)(u
82
+ u
81
+ ··· + 403u + 61)
c
7
(u
23
− u
22
+ ··· − 4u + 1)(u
82
+ 2u
81
+ ··· + 28u − 151)
c
8
(u
23
+ u
22
+ ··· − 3u − 1)(u
82
+ 6u
81
+ ··· − 11u − 3)
c
9
(u
23
+ 8u
21
+ ··· + u + 1)(u
82
+ u
81
+ ··· + 403u + 61)
c
10
(u
23
− 8u
21
+ ··· + 13u − 1)(u
82
− u
81
+ ··· − 2699225u + 632501)
c
11
, c
12
(u
23
− u
22
+ ··· − 3u + 1)(u
82
+ 6u
81
+ ··· − 11u − 3)
20
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
23
+ 7y
22
+ ··· + 8y −1)
· (y
82
+ 70y
81
+ ··· + 3143561008y + 225961024)
c
2
, c
5
(y
23
+ 13y
22
+ ··· − 418y −121)(y
82
+ 52y
81
+ ··· − 12412y + 441)
c
3
(y
23
+ 9y
22
+ ··· − 2y −1)
· (y
82
+ 48y
81
+ ··· − 10989606497604y + 891685492681)
c
4
(y
23
− 6y
22
+ ··· + 17y −1)
· (y
82
− 71y
81
+ ··· − 240578075y + 13082689)
c
6
, c
9
(y
23
+ 16y
22
+ ··· + y −1)(y
82
+ 47y
81
+ ··· + 37305y + 3721)
c
7
(y
23
− 7y
22
+ ··· − 8y −1)(y
82
+ 4y
81
+ ··· − 246310y + 22801)
c
8
, c
11
, c
12
(y
23
− 13y
22
+ ··· + 19y −1)(y
82
− 18y
81
+ ··· − 397y + 9)
c
10
(y
23
− 16y
22
+ ··· + 67y −1)
· (y
82
− 45y
81
+ ··· − 21983555058121y + 400057515001)
21
